08. Numeral Systems

Numeral Systems Binary, Decimal and Hexadecimal Numbers ,[object Object],[object Object],[object Object]

Table of Contents ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Numeral Systems Conversion between Numeral Systems

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Decimal Numbers

Binary Numeral System 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Binary Numbers

Binary to Decimal Conversion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Decimal to Binary Conversion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hexadecimal Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hexadecimal Numbers (2) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hexadecimal to Decimal Conversion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Decimal to Hexadecimal Conversion ,[object Object],[object Object],[object Object],[object Object]

Binary to Hexadecimal (and Back) Conversion ,[object Object],[object Object]

Numbers Representation Positive and Negative Integers and Floating-Point Numbers

Representation of Integers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Positive and Negative Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Positive and Negative Numbers (2) ,[object Object],[object Object],[object Object],[object Object]

Representation of 8-bit Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Floating-Point Numbers ,[object Object],[object Object],1 10000011 01010010100000000000000 Mantissa = 1,3222656 25 Exponent = 4 Sign = - 1 Bits [2 2 … 0 ] Bits [3 0 … 23 ] Bit 31 * See http://en.wikipedia.org/wiki/Floating_point 2 k - 1 2 0 2 - 1 2 - 2 2 - n S P 0 ... P k - 1 M 0 M 1 ... M n - 1 Sign Exponent Mantissa

Text Representation in Computer Systems

How Computers Represent Text Data? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Character Codes – ASCII Table Excerpt from the ASCII table Binary Code Decimal Code Character 01000001 65 A 01000010 66 B 01000011 67 C 01000100 68 D 0 0100011 35 # 011 0 0000 48 0 00110001 49 1 01111110 126 ~

Strings of Characters ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],… … … … … … … … 4 bytes length … … … … … …

Numeral Systems http://academy.telerik.com

Exercises ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Exercises (2) ,[object Object],[object Object],[object Object]

08. Numeral Systems

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08. Numeral Systems

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